Just two weeks ago, Republican Senators were boasting about big plans to spend $46 billion over the next 10 years to enhance security on the southern border. “Almost overkill,” Tennessee Republican Bob Corker said of the plan. “Well oversufficient,” added Arizona Republican John McCain. “We’ll be the most militarized border since the fall of the Berlin Wall.” The Senators meant this as a good thing.

But as the bill moves to the House, the excess is beginning to look like a liability. The deal, which helped pass the Senate rewrite of U.S. immigration laws, is unlikely to sway House Republicans who insist on securing the border before some 11 million undocumented immigrants can begin the naturalization process. And it is alienating allies who are vital to immigration reform’s chances in the House, including a prominent Latino advocacy group and at least one Democratic Representative.

In an unexpected wrinkle, even authorities on the border are balking, saying the influx of agents could create more problems than it would solve. “The majority of the sheriffs I’ve talked to are not in favor of an additional 19,000 border-patrol agents,” says Donald Reay, executive director of the Texas Border Sheriff’s Coalition, whose members are still weighing the Senate bill. Reay has concerns about where the agents would be stationed and the time it could take to perform background checks on so many new hires.

Shawn Moran, vice president of the National Border Patrol Council, says the union doesn’t support the spike in guards. “There’s nowhere to put them,” Moran says. “We’re just starting to get a handle on the 21,000 agents we have.” Noting the struggle to pay for salaries, guns, gas and office space for its existing members, Moran worries the sprint to recruit, hire and train new agents would result in a lower-quality force. “What we fear is that the agency would cut corners again in terms of the hiring and training. That would be a nonstarter for us.”

To win over a mere handful of Republicans, the Senate forked over $38 billion on top of its existing proposal to beef up the border. The plan, crafted by Corker and North Dakota Republican John Hoeven, would add about 20,000 agents and erect 700 miles of fencing along the 1,900-mile line between the U.S. and Mexico. “This was not done for policy reasons,” says Doris Meissner, director of U.S. immigration policy at the Migration Policy Institute and a former Immigration and Naturalization Service commissioner under President Clinton. “It was dictated by politics.”

To rally support for the measure, Hoeven argued that it would satisfy lingering concerns about security and enforcement. “The American people want a comprehensive immigration-reform plan with tough border enforcement,” he explained. “They want to know that 10 years from now, we won’t find ourselves in this same position, having to address the same problem.” But opponents of the surge say the debate in Washington, waged largely in abstractions, has ignored the realities of life on the border.

The number of agents stationed there has already quintupled over the past two decades, while spending on enforcement is 15 times higher than in 1986, the last time Congress overhauled U.S. immigration policy. Border cities are among the safest in the U.S. Illegal crossings have dipped in many notorious trouble spots. “It’s overkill,” says Tony Estrada, the sheriff of Santa Cruz County, nestled against the Arizona border south of Tucson. “Additional personnel is not going to solve the problem. Maybe it will diminish it, but illegal immigration and drugs are going to continue.”

The original Senate bill, which allotted $8 billion for security measures, was expected to curb illegal immigration about 25%, according to the nonpartisan Congressional Budget Office. The CBO predicts the Corker-Hoeven amendment to further limit illegal crossings, potentially halving the flow of undocumented immigrants. Whether these reductions are worth the amendment’s $38 billion tab is another question — and one supporters were able to duck. The cost will be covered, they argue, by the $135 billion the CBO projects the bill to save by 2023 through greater revenues produced by a larger legal labor force, including more-skilled immigrants earning higher wages.

While the push to double the number of border agents has done little to neutralize House Republicans’ objections, it has incensed some of the bill’s supporters on the left. Filemon Vela, a House Democrat from Texas, quit the Congressional Hispanic Caucus last week over the group’s implied support of the Senate bill. Vela did not respond to interview requests from TIME, but said in a floor speech that the beefed-up border presence would hamper the local economy and damage border communities.

The surge also prompted Presente.org, a Latino advocacy group that counts some 300,000 members, to withdraw its support for the Senate bill. “The bill has crossed the line,” Arturo Carmona, the group’s executive director, tells TIME. “We were willing to compromise on a right-of-center bill. At this point, it’s gone.”

“There’s no reform in this reform. We’re expected to just shut up and vote for it,” says one official with a liberal immigration-reform advocacy group. “Democrats think that if [immigration reform] passes, they win. And if it loses, they win, because they get to slam Republicans.” Barack Obama has presided over a higher rate of deportations than any President in history, the official notes, arguing that the bill’s lurch to the right jeopardizes Democrats’ support among a Latino community that is tired of being taken for granted.

“The whole deal is crafted on their backs,” says Adam Isacson, an expert at the Washington Office on Latin America, a policy group that studies human rights, social justice and security issues. Isacson argues that a beefed-up border-patrol presence could increase migrant deaths and abuse without stanching the flow of drugs or illegal immigrants into the U.S. “This has very little to do with what was good migration or border policy,” he says. “It was what could buy off the Republicans. This, it turns out, was the price.”

The tab could grow even steeper as the debate shifts to the House, where Republicans want even stronger border-security triggers. “They put the legalization of 11 million people ahead of security. The legalization happens first, and then the security happens second,” Idaho Republican Raúl Labrador said on NBC’s Meet the Press on Sunday. “I think the American people are not going to stand for that.”